# law of iterated expectations doubt

Is it correct to do so:

$$E(X^{-1} Y) = E_x(E(X^{-1} Y \vert X) = E_x(X^{-1} E(Y \vert X))$$

Are we allowed to use LIE in case of non linear functions like $$X^{-1}$$

• Yes, as $f(X)$ is constant conditional on $X$. – Xi'an May 16 at 20:23
• @Xi'an Thank you. – Raghav Goyal May 16 at 20:53